Vol. 28, No. 2, 1969

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Classes without the amalgamation property

Stephen Daniel Comer

Vol. 28 (1969), No. 2, 309–318

The contents of this paper belong to the general algebraic theory of those algebras which are studied in connection with algebraic logic. The main results, Theorems 1 and 2, give sufficient conditions for the amalgamation and the embedding property to fail in a class of Boolean algebras with operators. As a corollary, for 1 < α < ω, the amalgamation property fails in the class of all (representable) cylindric algebras of dimension α and in the class of all (representable) polyadic (equality) algebras of dimension α. Thus, there are finitely axiomatizable equational classes of Boolean algebras with operators for which the amalgamation property fails.

Mathematical Subject Classification
Primary: 02.50
Secondary: 08.00
Received: 22 February 1968
Published: 1 February 1969
Stephen Daniel Comer